How to always win at rock, paper, scissors

Thought rock, paper, scissors was a game of chance? Think again, says
William Poundstone

In 2005, a flagging Japanese economy convinced Takashi Hashiyama, president of the electronics firm Maspro Denkoh, to sell the corporate collection of French impressionist paintings.

This included a major Cézanne landscape and lesser works by Sisley, van Gogh, and Picasso. Both Christie’s and Sotheby’s gave presentations to Hashiyama touting their expertise and ability to achieve the highest auction prices. In Hashiyama’s judgment, the presentations were equally convincing. To settle the matter, he proposed a game of rock, paper, scissors.

“The client was very serious about this,” Christie’s deputy chairman Jonathan Rendell said, “so we were very serious about it, too.” The money was serious, too. The Maspro Denkoh collection was valued at $20 million. Both Christie’s and Sotheby’s quickly agreed to the game.

In case you never had a break at school, rock, paper, scissors (RPS) is a playground game as popular in the US and UK as it is in Japan (where it dates to the 18nth century at least). On a signal, two players simultaneously make one of three hand signs, chosen at will: rock (a fist); paper (an open hand, facedown, with fingers together); or scissors (a partial fist with the index and middle finger extended). An easily memorised rule determines the winner: “Rock breaks scissors, scissors cuts paper, paper covers rock.” In other words, a player who chooses rock beats one who chooses scissors; scissors in turn beats paper; paper beats rock. This yields a winner whenever the two players choose differently. When they choose the same sign, it’s a tie.

“There was some discussion” of strategies, Sotheby’s Blake Koh said. “But this is a game of chance, so we really didn’t give it that much thought. We had no strategy in mind.”

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In contrast, Kanae Ishibashi, the president of Christie’s Japan, began researching RPS strategies on the internet. You may or may not be surprised to learn that an awful lot has been written on the game. Ishibashi had a break when Nicholas Maclean, Christie’s director of impressionist and modern art, mentioned that his 11-year-old twin daughters, Alice and Flora, played the game at school almost daily.

Alice’s advice was “Everybody knows you always start with scissors.” Flora seconded this, saying “Rock is way too obvious. . . . Since they were beginners, scissors was definitely the safest.”

Both girls also agreed that, in the event of a scissors-scissors tie, the next choice should be scissors again — precisely because “everybody expects you to choose rock.”

Ishibashi went into the meeting with this strategy, while the Sotheby’s rep went in with no strategy at all. The auction house people sat facing each other at a conference table, flanked by Maspro accountants. To avoid ambiguity, the players wrote their choices on a slip of paper. A Maspro executive opened the slips. Ishibashi had chosen scissors, and the Sotheby’s representative had chosen paper. Scissors cuts paper, and Christie’s won.

In early May 2005, Christie’s auctioned the four paintings for $17.8 million, earning the auction house a $1.9 million commission.

A game of tactics

In college I knew a guy who had made a study of rock, paper, scissors. He assured me that the game was not as trivial as it seemed, and as proof he taught me a rather diabolical trick for winning bar tab bets with it. Good RPS players attempt to recognise and exploit unconscious patterns in their opponents’ play. That is anything but trivial. A World Rock Paper Scissors Society holds tournaments in Toronto. Though the media inevitably slots it under “news of the weird”, the coverage is usually deep enough to acknowledge the psychological elements.

The strategy for playing RPS depends on how skilled your opponent is. Let me start by giving a basic strategy for playing against a novice player (which is to say, 99 percent of the public).

First of all, the throws are not equally common. The World RPS Society reports these proportions (for tournament play, with mostly expert players):

Rock 35.4pc Paper 35.0pc Scissors 29.6pc

Though the names of the throws are arbitrary, they inherit cultural stereotypes. Rock is the testosterone choice, the most aggressive and the one favored by angry players. The majority of participants in RPS tournaments are male (is this a surprise to anyone?). On your first throw against an inexperienced male opponent, the best choice is paper because that will beat rock.

It’s said that women are most likely to throw scissors. You can supply your own psychoanalysis, but there aren’t enough women in RPS tournaments to make scissors as popular as the other choices.

Naïve players don’t like to repeat the same throw more than twice in a row. They can’t accept that as random. That means that a player who throws rock . . . rock . . . is more likely to switch to something else on the next throw.

This is a big deal in a game that’s nominally luck. The counterstrategy is to choose whatever sign the doubled sign would beat. Should your opponent throw rock . . . rock . . . you’d want to choose scissors on the next throw. Given that the opponent is unlikely to play rock again, scissors would be unbeatable. In case of paper, scissors wins; should the opponent choose scissors, it’s a tie.

RPS players mentally categorize their throws as winners and losers. A player who loses is more likely to switch to a different throw the next time. Some players unconsciously “copy” the sign that just beat them.

Doublethink and psych-outs

Expert RPS players have many other techniques. “I went in scripting only my first throw in my head,” 2008 USA Rock Paper Scissors League champion Sean Sears told me. “Then, depending on if it was a win, loss, or tie, I had the second throw scripted as well.” Like chess masters, good RPS players generally plan their openings and then quickly switch to improvisation.

Sears uses “pattern recognition” of the opponent’s moves as well as perceptions of his emotional state and likely strategies.

Trash talk is allowed in most tournaments, and honesty can be the most Machiavellian policy. Announce what sign you’re going to throw, and then throw it. This trips up the naïve player who figures you won’t go through with it. It’s the old mentalist trick of emphasizing an option in order to steer someone away from it.

Most good players believe in tells, or at any rate the possibility of tells. You should watch your opponent for any facial expressions or gestures that might betray the next move. Monica Martinez, 2008 winner of the World RPS Tournament, credited her victory to reading faces. “I didn’t worry about what I was going to do, I just did what I thought they were going to do.” Jonathan Monaco, winner of the 2009 USA RPS Tournament, wears dark sunglasses to make it harder for opponents to read his expression.

Players begin by priming, pumping their fists to a count of three. The throw usually comes on the fourth pump. Take note of whether the tip of the thumb is tucked in the crook of the index finger. Sometimes this is a giveaway. The tucked thumb often forecasts rock.

A really good player will know all of the above and will be thinking a step ahead . . . or not. This is the hall of mirrors that every serious strategist faces.

Never pay for a round of drinks again

If you play RPS as a grown‑up, it’s probably as a fair(?) way to decide who pays for drinks or gets an advantage in sports. You might want to remember this piece of advice that I learned from my college friend. When a suitable situation arises, you say, “Hey, let’s do rock, paper, scissors for it!” Without waiting for an okay, begin pumping your fist. One . . . two . . . three . . .

There’s a good chance your partner will join in. Then you throw paper.

The usual preference for rock is greatly enhanced when the player doesn’t have time to think. For the best odds, you should try this only with a male.

The safety net: In the event you lose, immediately start priming for the next throw. You’re going for two of three, of course.

Recap: How to always win at rock, paper, scissors

• Scissors is the least popular choice, and men favour rock. Both are reasons to choose paper in a one-shot match.

• Announce what you’re going to throw and do it. Most players figure you won’t go through with it.